few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Solve real-world and mathematical problems involving area, surface area, and volume.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand congruence in terms of rigid motions.

Prove geometric theorems.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Find arc lengths and areas of sectors of circles.

Make geometric constructions.

Understand and apply theorems about circles.

Classify two-dimensional figures into categories based on their properties.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Analyze, compare, create, and compose shapes.

Explain volume formulas and use them to solve problems.

Define trigonometric ratios and solve problems involving right triangles.

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

Translate between the geometric description and the equation for a conic section.

Reason with shapes and their attributes.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Apply geometric concepts in modeling situations.

Visualize relationships between two-dimensional and three-dimensional objects.

Understand and apply the Pythagorean Theorem.

Prove theorems involving similarity.
problem_activity: Activity
In this activity, students find the missing dimensions of cylinders when given the volume and the other dimension. A volume equation representing the cylinder is given for each problem.
Identify students who use these strategies: guess and check, divide each side of the equation by the same value to solve for missing variable, or use the structure of the volume equation to reason about the missing variable
Launch
Arrange students in groups of 2. Give students 2–3 minutes of quiet work time followed by time to share their explanation for the first problem with their partners.
Representation: Internalize Comprehension.
Activate or supply background knowledge of strategies students can use to solve for unknown variables in equations. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Writing, Conversing: MLR1 Stronger and Clearer Each Time.
Use this routine to give students a structured opportunity to revise a response to one or both of the questions. Ask each student to meet with 2–3 other partners in a row for feedback. Provide student with prompts for feedback that will help students strengthen their ideas and clarify their language (e.g., “What did you do first?”, “How do you know
\(h\)
is...?”, and “How did you use the volume formula?”, etc.). Students can borrow ideas and language from each partner to strengthen their final explanation.
Design Principle(s): Optimize output (for explanation)
Student Facing
The volume
\(V\)
of a cylinder with radius
\(r\)
is given by the formula
\(V=\pi r^2h\)
.
The volume of this cylinder with radius 5 units is
\(50\pi\)
cubic units. This statement is true:
\( 50\pi = 5^2 \pi h\)
[IMG]
What does the height of this cylinder have to be? Explain how you know.
The volume of this cylinder with height 4 units is
\(36\pi\)
cubic units. This statement is true:
\(36\pi = r^2 \pi 4\)
[IMG]
What does the radius of this cylinder have to be? Explain how you know.
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
Suppose a cylinder has a volume of
\(36\pi\)
cubic inches, but it is not the same cylinder as the one you found earlier in this activity.
What are some possibilities for the dimensions of the cylinder?
How many different cylinders can you find that have a volume of
\(36\pi\)
cubic inches?
Student Response
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for free access to Extension Student Response.
Activity Synthesis
Select previously identified students to explain the strategies they used to find the missing dimension in each problem. If not brought up in students’ explanations. Discuss the following strategies and explanations:
Guess and check: plug in numbers for
\(h\)
, a value that make the statements true. Since the solutions for these problems are small whole numbers, this strategy works well. In other situations, this strategy may be less efficient.
Divide each side of the equation by the same value to solve for the missing variable: for example, divide each side of
\(36\pi=r^2 \pi 4\)
by the common factor,
\(4\pi\)
. It’s important to remember
\(\pi\)
is a number that can be multiplied and divided like any other factor.
Use the structure of the equation to reason about the missing variable: for example,
\(50\pi\)
is double
\(25\pi\)
, so the missing value must be 2.


correct_option_index: 12